1. The absorption spectra of ions have been used to identify the presence of the
ID: 816861 • Letter: 1
Question
1. The absorption spectra of ions have been used to identify the presence of the elements in the atmospheres of the sun and other stars. What is the wavelength of light (in nm) that is absorbed by He+ ions, when an electron is excited from the Bohr orbit with n = 2 to the n = 7 state? The energy of an electron in the nth level is
2. An electron in the 4th energy level of the H atom drops to the 1st energy level. In other words an excited electron drops to the ground state. What is the energy (in J) of the emitted photon)? The energy of an electron in the nth level is
En = - BZ2 n2
Explanation / Answer
1.Z=2, so the equation is E=-4B/n^2
calculate the value of E when n=2 and when n=9
subtract these two energies, this represents the energy difference of the transition, call this energy delta E
the wavelength of the photon emitted in this transition is:
Delta E=2.18 x 10-18 (1/4-1/81)
lambda = h c/Delta E where h is Planck's constant = 6.62x10^(-34)Js and c is the speed of light = 3x10^8m/s
lambda=6.62x10^(-34)* 3x10^8/2.18 x 10-18 (1/4-1/81) =3.83*10^9m
2.
En=B/n^2
=(2.18 x 10-18) /n^2
E1-E4=
2.18 x 10-18 (1-1/16)
2.04*10^-18
3.E = nhf
n is the number of moles (one)
h is the Planck's constant (6.63 x 10^-34)
f is the frequency (8.40 x 10^14)
Hence, multiplying them together, energy E = 5.56 x 10 ^ -19 joules
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